Base Seattle is located in the SoDo district (South of Dome) at:
14 S Massachusetts St
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View Metro's web site at https://kingcounty.gov/depts/transportation/metro.aspx. Stadium Station on the Light Rail is an approximately 20 minute walk to Base Seattle. Many buses also terminate in the Pioneer Square/SoDo/International District area with a similar walk. A small number of buses serve stops on 1st Ave S closer to Base Seattle, such as the 21 which runs from West Seattle to Downtown. Other routes that serve these stops are more limited.
Regional transit agencies include Community Transit (Snohomish County) at https://www.communitytransit.org/ and Sound Transit (regional in King, Pierce and Snohomish counties) at https://www.soundtransit.org/.
Check directions on a mapping service such as https://www.google.com/maps, as active construction in this area may change walking routes. Be aware of both train and semi truck traffic, and always use marked crosswalks. The flyover that goes up and over the viaduct along S. Atlantic St. has a sidewalk and is a good walking route when the direct route underneath the viaduct is blocked by a train.